Transcript Envision Math Presentation, October 20, 2016

Elementary Mathematics Today:
Balancing Understanding, Skills, &
Applications
Dr. Janet H. Caldwell
[email protected]
Math Practice Standards
3. Construct viable arguments and critique the
reasoning of others.
6. Attend to precision.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
Content Standards
K-5
Grade
Domain
K
Counting & Cardinality
K-5
Operations & Algebraic Thinking
Number & Operations in Base Ten
Measurement & Data
Geometry
3-5
Number & Operations – Fractions
Kindergarten
Early Number Relationships
Anchors to 5 and 10
Early Number Relationships
Part-Part-Whole
8
Grade 1
Grade 2
Adding within 100
25
+ 17
Toward Computational
Fluency
Addition & Subtraction of Whole Numbers
Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Understand
Facts to 20
Add with & without regrouping to 100
Subtract multiples of 10
Add up to four 2-digit numbers
Add & subtract up to 3 digits
Fluent within 1000
Fluency with standard algorithms
Grade 3
Grade 4
Computational Fluency
7 x 28
Using Base Ten Blocks to Multiply
24
x3
12
60
72
Make an Array
24
x3
12
60
72
A Harder Problem
24
x 13
12
60
40
200
312
Multiplication & Division
Grade 2
Introduction to multiplication
Grade 3
Understand
Facts
1 digit x multiple of 10
Grade 4
Using multiplication to compare
1 digit x up to 4 digits
2 digits x 2 digits
Up to 4 digits divided by 1 digit
Grade 5
Fluency with multiplication – standard algorithm
Up to 4 digits divided by 2 digits
Grade 6
Fluency with division – standard algorithm
Grade 5
Fractions
Grade 1
Partition circles & rectangles (2, 4)
Grade 2
Equal shares not always same shape;
Number of pieces in whole (2, 3, 4)
Grade 3
Unit fractions, fractions on a number line,
equivalence, comparison (2, 3, 4, 6, 8)
Grade 4
Equivalence, ordering,
Build fractions from unit fractions
Add & subtract like fractions & mixed numbers
Multiply fractions and whole numbers
Convert fractions to decimals (simple)
(2, 3, 4, 5, 6, 8, 10, 100, 12)
Grade 5
Add, subtract, & multiply fractions & mixed #s
Divide unit fractions & whole numbers
Grade 6
Divide fractions & mixed numbers
What We Have Learned about
Mathematics Education
• Students must learn basics, but
knowing the basics alone is not enough.
• Learning mathematics with
understanding is essential to enable
students to solve new problems.
• Students learn mathematics primarily by
doing mathematics rather than just
listening and memorizing.
“Understanding is the key to
remembering what is learned
and being able to use it
flexibly.”
- Hiebert, in Lester & Charles,
Teaching Mathematics through
Problem Solving, 2004.
Lesson Structure Overview
Warm-up, Review, Homework
1. Solve & Share
2. Visual Learning
• Practice
3. Assess & Differentiate
• Summary
Why Problem- Based Learning
• Students solve the problem any way they
choose.
• Introduces new math ideas in context
• Motivates new learning
• Recalls prior learning (coherence)
• Engages students in thinking about math
• Requires students to communicate
• Introduces or develops math representations
• Fosters reasoning skills
Solve & Share - Grade 1
Grade 4
Visual Learning
• Visual Learning
Animation
Everybody needs at least some…..
PRACTICE WITH
UNDERSTANDING
Assess & Differentiate
•
•
•
•
•
•
Quick Check
Intervention Activity
Reteach Worksheet
Centers (Intervention, Games)
Math & Science Activity (2/topic)
Technology (Tools, Games)
Summary
• Discuss essential question
• Assign homework as appropriate
Focus on Skills
Problem Solving
Bar Diagrams
Multiplication & Division
Balance is Critical
Applications
Concepts
Skills
At Home
• Use math in everyday activities.
• Talk about using math.
• Play math games.
-
Any game where you roll two dice and add.
Card games
Commercial games (e.g., 24, SET, BLINK)
On-line games
Helping with Homework
•
•
•
•
•
•
Ensure your child works on it.
Be positive!
Math makes sense.
Ask questions and listen.
Use resources.
Ask your child to explain thinking.
Resources for Parents
• https://www.youcub
ed.org/parents/
• Pearsonrealize.com
Questions?